Unable to edit individual objects made by the Array modifier
This is intended functionality - it is supposed to work like that. An array modifier makes an array of a single object so if you change that object, all the array is supposed to change as well. 

You can apply the modifier and edit the generated geometry as you wish or if you wish to have multiple objects you can duplicate them with Shift+d. If you perform the transforms with the duplicate operator(move or scale or rotate the object right after pressing Shift+d before confirming it) you can then repeat the action with Shift+r to make an array quickly. 

I assume that by 'edit' you mean going into edit mode and changing the geometry. You can still influence, deform or even change the geometry of parts of the object that is generated with the Array modifier by using other modifiers without editing the actual original object: